Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C3⋊(#1790⋊C3) |
| unambiguous semidirect product | #72142⋊C3 |
| derived | C3×H(5,𝔽2) ⋊ C3×C4 |
336 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2,3,2^5,3,2|a^2=c,d^a=df,e^a=efg,h^a=h^2,d^b=de,e^b=d,f^b=gi,g^b=fgi,g^d=gi,f^e=fi,g^e=gi54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154190);